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When I said runner, I imagined the core gameplay staying the same. The player would still be navigating a grid and dodging attacks in exactly the same way.  I wasn't thinking about how that might break the immersion and mess with the feel of attacks coming from fixed positions as you are visually moving forward. That suggestion came from seeing this statue at the top of the screen and thinking how cool it would feel to be moving towards some gargantuan, epic landmark compared to already being in front of it. So, a room or board based progress would probably fit much better. 

As to fun factor, I could enjoy a game with these gameplay bones, but what's layered on top would matter. 

Feeling of progress - playthroughs earn points/currency used to increase stats or buy moves, new characters, etc. Have endless/challenge modes, but also a main story/mission mode.

Atmosphere. I do like the statue, and I think telling me some wizard or demon uses the statue to "see" and "have power over" their territory would make me feel really cool if I was going from castle to castle breaking statues to weaken the villain's influence over the world. Castle-anthem music (in my mind, like  from 8/16-bit Mario castle/Zelda dungeon themes or Castlevania SoTN or older) would help me get into it, especially if attacks were on-beat, because it creates a really cool way for me to zone into a game.

A real gameplay hook. Like, the closer calls are with your dodging, the more it charges an "ultimate" bar that clears the level, unlocks a tool or a move, or activates a score multiplier. Give players a risk/reward way to show off and get an extra rush. 

Movement feel. Grid-based hopping can only vary so much, but faster/slower/instant hopping response, a minimum pause between moves (small, like .1 seconds-ish), can make a big difference, as can if a player's presses are either only taken one at a time when the hero is ready, or if they're buffered (like if I can push up up up right right all during the character's 1st move but the character completes the rest of the moves anyway) Yeah, that may sound weird.

As I was typing this, I was reminded of Guidus, available at least on mobile. Your game is structured differently, but I think Guidus' similarities might give you perspective . It's a simple grid-based hopping dungeon crawler roguelike packed with features and layers on a very simple game that is very fun to play and play and replay.